O-LevelMathematicsCoordinate geometry4024/22 · Oct/Nov 2025 · Q189 Marks

The equation of line L is y = x/5 + 3.

(a)Write down the gradient of line L.[1]
(b)(i)Line M is parallel to line L. Line M crosses the x-axis at point A and the y-axis at point B. The coordinates of point A are (15,0). Show that the coordinates of point B are (0, -3).[3]
(b)(ii)Line N is the perpendicular bisector of the line joining point A and point B. Line N crosses the x-axis at point C. Find the coordinates of point C.[5]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

[1] 1/5 oe
[1] M1 for Gradient of line M = their -1/5 oe
[1] M1 for Substitutes (15, 0) into their equation 0 = their gradient ×15+ c or y-0 = their gradient (x-15)
[1] Correct working leading to (0, -3) Dep on M1M1, A0 if any errors
[5] (7.2 oe, 0). B4 for y = −5x + 36 oe OR B1 for midpoint = (7.5, –1.5) oe soi
[1] M1 for gradient N = -1 / (their 1/5)
[1] M1 for substituting their (7.5, -1.5) in y = (their -5)x + c oe
[1] M1dep for substituting y = 0 in their y = -5x + 36

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